which of the following shows the factorization of $x^3 - x^2 + 2x - 2$?

a) $(x^2 + 2)(x + 1)$
b) $(x^2 + 2)(x - 1)$
c) $(x + 2)(x - 1)$
d) $(x + 2)(x + 1)$

question 13 (5 points)
consider points $a$, $b$, and $c$ in the graph. which point is the global maximum?

a) none of these
b) $a$
c) $b$
d) $c$

Question

which of the following shows the factorization of $x^3 - x^2 + 2x - 2$?

a) $(x^2 + 2)(x + 1)$
b) $(x^2 + 2)(x - 1)$
c) $(x + 2)(x - 1)$
d) $(x + 2)(x + 1)$

question 13 (5 points)
consider points $a$, $b$, and $c$ in the graph. which point is the global maximum?

a) none of these
b) $a$
c) $b$
d) $c$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring by Grouping", "Relative Extrema" ], "new_concepts": [], "current_concepts": [ "Factoring by Grouping", "Relative Extrema" ] } ## Factor the polynomial by grouping $$ \begin{aligned} x^3 - x^2 + 2x - 2 &= (x^3 - x^2) + (2x - 2) \ &= x^2(x - 1) + 2(x - 1) \ &= (x^2 + 2)(x - 1) \end{aligned} $$ ## Identify the global maximum point from the graph $$ \begin{aligned} &\text{Point } a \approx (0.5, 2.25) \ &\text{Point } b \approx (1, 2) \ &\text{Point } c \approx (-1.5, -2) \ &y_a > y_b > y_c \implies \text{Point } a \text{ is the global maximum} \end{aligned} $$ ## Question 1 A) $(x^2 + 2)(x + 1)$

B) $(x^2 + 2)(x - 1)$

C) $(x + 2)(x - 1)$

D) $(x + 2)(x + 1)$ ## Question 2 A) None of these

B) a

C) b

D) c

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring by Grouping" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the polynomial by grouping

Identify the global maximum point from the graph

Answer:

Question 1

Question 2